1. Consider a cube with vertices at A=(0,0,0) B=(2,0,0) C=(2,2,0) D=(0,2,0) E=(0,0,2) F=(2,0,2) G=(2,2,2) H=(0,2,2)
A)Calculate the flux of the vector field
F=x
i through each face of the cube by taking the normal vectors pointing outwards.
B)Verify Gauss's divergence theorem for the cube and the vector field
F by computing each side of the formula.
C)Using Gauss's divergence theorem evaluate the flux
of the vector field
F=x
i+y
j+
k where S is a closed surface consisting of the cylinder
, 0<z<b and the circular disks
at z=0 and
at z=b.
I have the basics but dont know how to get an answer. My workings are attatched.